We give the complete list of 175 facet Bell inequalities for the case where Alice and Bob each choose their measurements from a set of four binary outcome measurements. For each inequality we compute the maximum quantum violation for qubits, the resistance to noise, and the minimal detection efficiency required for closing the detection loophole with maximally entangled qubit states, in the case where both detectors have the same efficiency (symmetric case).

Spontaneous symmetry breaking (SSB) is mathematically tied to either the thermodynamic or the classical limit, but physically, some approximate form of SSB must occur before the limit. For a Schroedinger operator with double well potential in the classical limit, this may indeed be accomplished by the “flea” mechanism discovered in the 1980s by Jona-Lasinio et al. We adapt this mechanism to the Curie-Weiss model (as a paradigmatic mean-field quantum spin system), and also establish an unexpected relationship between this model (for finite N) and a discretized Schroedinger operator with double well potential.

Quantum cognition is an emerging field making uses of quantum theory to model cognitive phenomena which cannot be explained by classical theories. Usually, in cognitive tests, subjects are asked to give a response to a question, but in this paper, we just observed the subjects’ behaviour and the question and answer method was not applied in order to prevent any mental background on participants’ minds. Finally, we examined the experimental data on Hardy’s non-locality argument (HNA), and we noticed the violation of HNA in human behaviour.

We present here a quantum cosmological model with Bohm-de Broglie interpretation of the theory described by a combination of two terms of the Fab Four cosmological theory. The first term is the John Lagrangian and the second is a potential representing matter content to avoid classical trivial solutions. This model has two free functions that provide an adjustment mechanism known classically as self-tuning. The self-tuning is a way to address the cosmological constant problem by allowing a partial break of symmetry in the scalar field sector. The Fab Four is the most general set of self-tuning scalar-tensor gravitational theories in four dimensions. The minisuperspace Hamiltonian thus obtained from this combination of Fab Four terms has fractional powers in the momenta, leading to a problem in applying canonical quantization. We have solved this problem by generalizing the canonical quantization rule using the so-called conformable fractional derivative. We show that this analysis leads to both singular and bouncing (non-singular) solutions, depending on the initial conditions over the scale factor and the homogeneous scalar field, and also depending on the free functions mentioned. This provides an adjustment mechanism in analogy with the classical self-tuning of the Fab Four, but with another interpretation.

Computer simulations allow us to explore non-perturbative phenomena in physics. This has the potential to help us understand quantum gravity. Finding a theory of quantum gravity is a hard problem, but in the last decades many promising and intriguing approaches that utilize or might benefit from using numerical methods were developed. These approaches are based on very different ideas and assumptions, yet they face the common challenge to derive predictions and compare them to data. In March 2018 we held a workshop at the Nordic Institute for Theoretical Physics (NORDITA) in Stockholm gathering experts in many different approaches to quantum gravity for a workshop on “Quantum gravity on the computer”. In this article we try to encapsulate some of the discussions held and talks given during this workshop and combine them with our own thoughts on why and how numerical approaches will play an important role in pushing quantum gravity forward. The last section of the article is a road map providing an outlook of the field and some intentions and goalposts that were debated in the closing session of the workshop. We hope that it will help to build a strong numerical community reaching beyond single approaches to combine our efforts in the search for quantum gravity.

Black hole (BH) thermodynamics was established by Bekenstein and Hawking, who made abstract theoretical arguments about the second law of thermodynamics and quantum theory in curved spacetime respectively. Testing these ideas experimentally has, so far, been impractical because the putative flux of Hawking radiation from astrophysical BHs is too small to be distinguished from the rest of the hot environment. Here, it is proposed that the spectrum of emitted gravitational waves (GWs) after the merger of two BHs, in particular the spectrum of GW150914, can be used to infer a lower limit on the magnitude of the entropy of the post-merger BH. This lower bound is significant as it is the same order as the Bekenstein-Hawking entropy. To infer this limit, we first assume that the result of the merger is an ultracompact object with an external geometry which is Schwarzschild or Kerr, but with an outer surface which is capable of reflecting in-falling GWs rather than fully absorbing them. Because of the absence of deviations from the predictions of general relativity in detected GW signals, we then obtain a bound on the minimal redshift factor of GWs that emerge from the vicinity of the object’s surface. The lack of deviations also means that the merger remnant essentially needs to have an absorbing surface, and thus it must effectively be a BH. Finally, a relationship between the minimal redshift factor and the BH entropy, which was first proposed by ‘t Hooft, is used to set a lower bound on the entropy of the post-merger BH.

Abstract

The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs’ general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must, the fundamentally statistical character of quantum mechanics. This is illustrated by drawing an analogy with an ideal gas. An ensemble interpretation of the Schrödinger cat experiment that does not violate the PBR conclusion is also given. The ramifications, limits, and weaknesses of the PBR assumptions, especially in light of lessons learned from Bell’s theorem, are elucidated. It is shown that, if valid, PBRs’ conclusion specifies what type of ensemble interpretations are possible. The PBR conclusion would require a more direct correspondence between the quantum state (e.g., \( \left| {\psi \rangle } \right. \) ) and the reality it describes than might otherwise be expected. A simple terminology is introduced to clarify this greater correspondence.

Abstract

Monism is roughly the view that there is only one fundamental entity. One of the most powerful argument in its favor comes from quantum mechanics. Extant discussions of quantum monism are framed independently of any interpretation of the quantum theory. In contrast, this paper argues that matters of interpretation play a crucial role when assessing the viability of monism in the quantum realm. I consider four different interpretations: modal interpretations, Bohmian mechanics, many worlds interpretations, and wavefunction realism. In particular, I extensively argue for the following claim: several interpretations of QM do not support monism at a more serious scrutiny, or do so only with further problematic assumptions, or even support different versions of it.

https://doi.org/10.22331/q-2018-11-27-108Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.